Vorticity internal transition layers for the Navier-Stokes equations
Journées équations aux dérivées partielles (2008), article no. 8, 15 p.

We deal with the incompressible Navier-Stokes equations, in two and three dimensions, when some vortex patches are prescribed as initial data i.e. when there is an internal boundary across which the vorticity is discontinuous. We show -thanks to an asymptotic expansion- that there is a sharp but smooth variation of the fluid vorticity into a internal layer moving with the flow of the Euler equations; as long as this later exists and as t<<1/ν, where ν is the viscosity coefficient.

@article{JEDP_2008____A8_0,
     author = {Sueur, Franck},
     title = {Vorticity internal transition layers for the Navier-Stokes equations},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     publisher = {Groupement de recherche 2434 du CNRS},
     year = {2008},
     doi = {10.5802/jedp.52},
     language = {en},
     url = {http://www.numdam.org/item/JEDP_2008____A8_0}
}
Sueur, Franck. Vorticity internal transition layers for the Navier-Stokes equations. Journées équations aux dérivées partielles (2008), article  no. 8, 15 p. doi : 10.5802/jedp.52. http://www.numdam.org/item/JEDP_2008____A8_0/

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